I stick with a 16-segment cylinder, and my base consists of two parts, where the upper “disk” is floating freely.
Yes, physically impossible, i know 
but i want to place a very soft blue LED-like light in this space in the middle to make them glow (the white figures) and a red LED on the black figures.
It (hopefully) looks like a scifi-chess set — maybe I build the 3D chess of Mr Spock here 